High regression rate hybrid rocket propellants and method of selecting

ABSTRACT

This invention comprises a new process for developing high regression rate propellants for application to hybrid rockets and solid fuel ramjets. The process involves the use of a criterion to identify propellants which form an unstable liquid layer on the melting surface of the propellant. Entrainment of droplets from the unstable liquid-gas interface can substantially increase propellant mass transfer leading to much higher surface regression rates over those that can be achieved with conventional hybrid propellants. The main reason is that entrainment is not limited by heat transfer to the propellant from the combustion zone. The process has been used to identify a new class of non-cryogenic hybrid fuels whose regression rate characteristics can be tailored for a given mission. The fuel can be used as the basis for a simpler hybrid rocket design with reduced cost, reduced complexity and increased performance.

GOVERNMENT LICENSE RIGHTS

[0001] The U.S. Government has a paid-up license in this invention andthe right in limited circumstances to require the patent owner tolicense others on reasonable terms as provided for by the terms ofContract/Grant No. NCC8-30-TRP, 10341 awarded by the NationalAeronautics and Space Administration.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of U.S. Provisional PatentApplication No. 60/093,696, filed Jul. 22, 1998, the entire disclosureof which is incorporated herein by reference.

FIELD OF THE INVENTION

[0003] The present invention relates generally to the field ofpropellants suitable for use in hybrid rockets, and more particularly topropellants and a method of selecting propellants that exhibit highregression rates.

BACKGROUND OF THE INVENTION

[0004] Two basic types of chemical rocket propulsion systems are widelyused in the rocket industry; namely, liquid systems and solid propellantsystems. In a liquid system, liquid oxidizer and liquid fuel are fed athigh pressure to a combustion chamber where they mix and react producinghigh temperature, high pressure gases which exhaust through aconverging-diverging nozzle producing thrust. The mixing of reactantsrequires a high performance pressurization system for the fuel andoxidizer which must often operate in a cryogenic environment at extremepressures and mass flow rates. The injection system and combustionchamber require exotic materials, complex systems for cooling, and veryhigh precision manufacturing techniques. All of these factors contributeto a high cost.

[0005] Solid propellant systems do not require the complex and expensivemachinery of liquid systems. Nevertheless, solid systems arecomplicated, and are subject to the difficulties of producingcrack-free, repeatable, fuel grains, and by the need to transport andhandle explosive materials. In a manufacturing process that requiresextreme safety precautions, solid fuel and oxidizer are intimately mixedand allowed to cure inside the rocket case producing an explosive fuelwith roughly the consistency of plastic or hard rubber. Fuel grainswhich contain cracks present a risk of explosive failure of the vehicleand must be rejected, driving up the cost of manufacture. Upon ignitionthe solid fuel burns uninterrupted until all the fuel is exhausted.

[0006] An alternative chemical rocket which has been known since the1930's is the hybrid propulsion system. In the hybrid design onepropellant is stored in the solid phase while the other is stored in theliquid phase. Thus the hybrid lies somewhere between the two basicchemical rocket designs just described. In most hybrid propulsionapplications, the solid is the fuel and the liquid is the oxidizer.Reverse hybrids with the fuel in the liquid phase and oxidizer in thesolid phase are also feasible and the present invention described belowcan be applied equally well to both types of hybrid systems.

[0007] A large variety of fuels, including trash and wood, have beenconsidered for hybrid rockets but the most conventional fuel materialsare polymers such as Plexiglas (polymethyl methacrylate) (PMMA), highdensity polyethylene (HDPE), hydroxyl terminated polybutadiene (HTPB),and the like. Typical oxidizers that are frequently used in hybridrockets are liquid oxygen, hydrogen peroxide, nitrogen tetroxide,nitrous oxide and occasionally fluorine. With respect to the last point,the fuel combinations used for hybrids are similar in their chemicalproperties and energy densities to the fuels used in hydrocarbon fueledliquid rocket systems. Thus, in terms of exhaust velocity and specificimpulse, the hybrid system is a closer relative to a liquid system thanto a solid system. Solid rockets tend to use lower energy oxidizers andconsequently they produce lower specific impulse.

[0008] In addition to having a higher specific impulse, some of theadvantages of the hybrid rocket over the solid fuel rocket are:

[0009] The hybrid allows for thrust termination, restart and throttlingcapabilities,

[0010] The hybrid design lends itself to safe manufacturing,transportation and operation.

[0011] Hybrid motors are inherently immune to explosion,

[0012] The safety and simplicity of the hybrid leads to lowerdevelopment costs for new systems and very likely lower operationalcosts,

[0013] The combustion products are generally very benign producing lowerenvironmental impact.

[0014] The main advantages of the hybrid over the liquid rocket include:

[0015] Lower development and operating costs (life cycle costs),

[0016] Lower fire and explosion hazards,

[0017] Less complex design and potentially higher reliability.

[0018] The hybrid allows the addition of energetic solid components,such as aluminum or beryllium to the fuel.

[0019] A schematic of a typical hybrid propulsion system 10 with apressurized oxidizer feed system is shown in FIG. 1. The feed system iscomprised of a pressurization tank 12 that holds an inert gas at highpressure (such as Helium, Argon or Nitrogen), a valve (not shown) topressurize the oxidizer tank 14, a main valve 16 to turn on the flow ofoxidizer and an injection system 18. Alternatively, the gaspressurization system can be replaced with a turbopump. The other majorcomponents are the combustion chamber 20 which contains the solid fuel22 and the nozzle assembly 24.

[0020] A sketch of the flame configuration in a single port hybridrocket combustion chamber 30 is shown in FIG. 2. The single portcombustion chamber 30 generally includes a pre-combustion chamber region31 at the front end, a post-combustion chamber region 32 at the oppositeend, and an elongated single port 33 extending between the ends. Theoxidizer in the liquid phase is injected into the combustion chamber atpre-combustion chamber region 31. The injected oxidizer is gasified andflows axially along the port 33, forming a boundary layer 34 over thesolid fuel 22. The boundary layer 34 is usually turbulent in nature overa large portion of the length of the port. Within the boundary layer 34there exists a turbulent diffusion flame 36 which extends over theentire length of the fuel. The thickness of the flame is generally verysmall compared to the boundary layer thickness. The heat generated inthe flame, which is located approximately 20-30% of the boundary layerthickness above the fuel surface, is transferred to the wall mainly byconvection. Some heat is also transferred by radiation but this isusually relatively small compared to the convective heat transfer. Inthe conventional hybrid system depicted in FIG. 2, the wall heat fluxevaporates the (generally polymeric) solid fuel and the fuel vapor istransported to the flame where it reacts with the oxidizer which istransported from the free stream by turbulent diffusion mechanisms. Theunburned fuel that travels beneath the flame, the unburned oxidizer inthe free stream, and the flame combustion products mix and further reactin the post combustion chamber 32. The degree to which fuel and oxidizerare able to fully mix and react before exhausting through the nozzle 24determines the combustion efficiency of the motor. The hot gases expandthrough a convergent-divergent nozzle 24 to deliver the required thrust.

[0021] It is important to note that, even though the geometry of ahybrid motor is similar to a solid motor, the combustion scheme isvastly different. In a solid rocket, the oxidizer and fuel are bothstored in the solid phase next to each other for heterogeneous fuels andwithin the same fuel molecule for double base fuels. Consequently, thesolid combustion takes place in a deflagration (premixed) flame that iscloser to the surface compared to the hybrid diffusion flame. Also, insolid fuel systems there exists some heterogeneous phase (solid-solid,solid-gas) reactions at the surface. In short, the burning rate of asolid rocket is determined by the rate of homogeneous (gas phase) andheterogeneous chemical reactions.

[0022] In a hybrid system or motor, the burning rate is limited by theheat transfer from the relatively remote flame to the burning surface ofthe fuel. One of the physical phenomena that limits the burning rate ina hybrid motor is the so-called blocking effect that is caused by thehigh velocity injection of the vaporizing fuel into the gas stream. Thisdifference in the combustion scheme of a hybrid motor significantlyalters the burning rate characteristics compared to a solid rocket.Blocking can be explained as follows. Increasing the heat transfer tothe fuel causes the evaporative mass transfer from the liquid-gasinterface to increase. But the increased blowing from the surfacereduces the temperature and velocity gradient at the surface thusreducing the convective heat transfer. The blowing also thickens theboundary layer and displaces the flame sheet further from the fuelsurface leading to a further reduction in convective heat transfer. Theposition of the flame sheet and the shape of the thermal and velocityboundary layer is the result of a complex chemical and fluid mechanicalbalance between the oxidizer flow entering the port, the fuel flowproduced by evaporation and the flow of combustion products. As aresult, the burning rate is limited in a fundamental way which isdifficult to overcome by either increasing heat transfer to the fuel orby a reduction in the fuel heat of gasification. Although radiative heattransfer from the flame does not suffer from the blocking effect it isusually small compared to the convective heat transfer. The upshot ofall this is that the regression rate, defined as the recession speed ofthe solid surface of a conventional hybrid fuel is typically one-tenthor less than that of a solid rocket fuel.

[0023] For a given selection of fuels and oxidizer to fuel mass ratio,the thrust generated by a rocket is approximately proportional to themass flow rate. Thus a given thrust requirement dictates the fuel massflow rate that needs to be achieved. The fuel mass flow generation rateis a product of the fuel density times the regression rate, multipliedby the burning surface area. The fuel density is determined by the typeof fuels. Generally, high thrust levels are required for a launchvehicle. For a hybrid rocket design based on a slow burning conventionalfuel, high thrust can only be achieved by increasing the burning surfacearea. The high burning area requirements, and various other designconstraints (such as the maximum grain length to port diameter ratio),leads to complicated multi-port configurations. One commonly usedmulti-port configuration is the wagon wheel geometry as shown in FIG. 3,and has been implemented in several hybrid motor designs.

[0024] The wagon wheel configuration and all other complicatedmulti-port designs have serious disadvantages. These disadvantagesinclude:

[0025] the large sliver fractions, which may in practice leavesignificant amounts of fuel unburned;

[0026] fairly small volumetric loading of the fuel in the casing leadingto decreased mass fractions;

[0027] grain integrity problems, especially towards the end of the burnwhen the web thickness between ports becomes vulnerable to structuraldisintegration;

[0028] difficult and expensive manufacturing of the fuel grain; and

[0029] requirement for a pre-combustion chamber or multiple injectors.

[0030] It is clear that all these factors seriously degrade the overallefficiency and cost of a multi-port hybrid launch vehicle.

[0031] The low regression rates and consequent multi-port designrequirements make hybrids an unattractive option, even though they offersignificant advantages over currently used liquid and solid systems. Inorder for the hybrid to find use as a practical design with a variety ofapplications, higher regression rates are required. Thus, so far manytechniques have been suggested, or tried, to improve the regressionrates of hybrids, however all of these techniques suffer importantshortcomings. More specifically, one such prior art method uses fuelswith low effective heat of gasification. This method yields only a smallimprovement since, as revealed in the classical hybrid theory (reference1), the exponent of the heat of gasification is a small number(approximately 0.32). The weak dependency of the regression rate on theheat of gasification is due to the blocking effect described earlier.Other prior art techniques use insertion of screens in the port toincrease the turbulence level, and thus the heat transfer rates. As withany method which requires that devices be placed in the gas flow path,this method complicates the design significantly and increases thelikelihood of failure. In addition, this approach may lead to nonuniformburning along the port.

[0032] The addition of swirl to the incoming oxidizer flow to increasethe effective mass flux and thus improve the heat transfer rate has alsobeen reported (Reference 8). This method also complicates the hybriddesign, especially for large scale motors, and requires heavy injectorsor vanes.

[0033] Another prior art approach employs the addition of oxidizingagents or self decomposing materials in the hybrid fuel. This well knowntechnique reverts to a quasi-solid design and eliminates the inherentsafety characteristic of hybrid rockets.

[0034] The addition of metal additives has also been used. This is acommon technique that improves the fuel mass burning rate. Theimprovement is small, however, and there are several shortcomings suchas the increased vulnerability to instabilities due to the pressuredependent regression rate and increased environmental impact.

[0035] Yet another prior art technique focuses on increasing theroughness of the burning surface by adding dispersed phase particles inthe fuel that would burn at a different rate compared to the matrixmaterial (Reference 9). This technique can only give a limitedimprovement and large solid particles injected in the gas stream reducethe efficiency of the system. The manufacturing costs would alsoincrease.

[0036] As just described, the prior art techniques are subject tosignificant limitations and disadvantages. Accordingly, it is highlydesirable to provide a propellant and hybrid system which exhibits ahigh regression rate, without compromising safety or manufacturing cost.

RELEVANT LITERATURE

[0037] [1] Marxman G. A., C. E. Wooldridge and R. J. Muzzy,“Fundamentals of Hybrid Boundary Layer Combustion”, Progress inAstronautics and Aeronautics, Vol.15, 1964 p 485.

[0038] [2] Karabeyoglu M. A., “Transient Combustion in Hybrid Rockets”,Stanford University Ph.D. Thesis, August 1998.

[0039] [3] Gater R. A. and M. R. L'Ecuyer, “A Fundamental Investigationof the Phenomena that Characterize Liquid Film Cooling”, InternationalJournal of Heat and Mass Transfer Vol. 13, pp 1925-1939, 1970.

[0040] [4] Ishii M. and M. A. Grolmes, “Inception Criteria for DropletEntrainment in Two Phase Concurrent Film Flow”, AICh Journal, vol. 21,no. 2, pp. 308-318, 1975.

[0041] [5] Nigmatulin R., B. Nigmatulin, Y A. Khodzaev and V. Kroshilin,“Entrainment and Deposition Rates in a Dispersed-Film Flow”,International Journal of Multiphase Flow Vol. 22, pp. 19-30, 1996.

[0042] [6] Bicerano, J, “Prediction of Polymer Properties”, MarcelDekker Inc., 1996.

[0043] [7] Dauber, T. E., Danner, R. T., “Physical and ThermodynamicProperties of Pure Chemicals, Data Compilation”, Taylor and Francis,1997.

[0044] [8] W. H. Knuth, M. J. Chiaverini, D. J. Gramer and J. A. Saver,“Solid-Fuel Regression Rate and Combustion Behavior of Vortex HybridRocket Engines”, Thirty-fifth Joint Propulsion Conference and Exhibit,AIAA Paper No. 99-2318, 1999.

[0045] [9] D. B. Stickler, “Heterogeneous Fuel for Hybrid Rocket”, U.S.Pat. No. 5,529,648 issued Jun. 25, 1996.

[0046] [10] DeRose, M. E., K. L. Pfeil, P. G. Carric and C. W. Larson,“Tube Burner Studies of Cryogenic Solid Combustion”, AIAA/SAE/ASME/ASEEThirty-third Joint Propulsion Conference and Exhibit, AIAA Paper No.97-3076, July 1997.

OBJECTS AND SUMMARY OF THE INVENTION

[0047] Accordingly, it is an object of the present invention to providehybrid rocket propellants that exhibit a high regression rate, or morespecifically, that will burn several times faster than conventionalpropellants at the same operating conditions of port mean mass flux andchamber pressure while retaining the basic advantages of hybrids;throttlability, safety and low cost. In addition to a high burning rateit is desired, but not required, that the propellant have the followingcharacteristics:

[0048] self-decomposing materials are not involved;

[0049] the port design can be structurally simple;

[0050] the propellant is safe, easy to handle and easy to process;

[0051] the propellant bums smoothly; and

[0052] the burning rate is reasonably uniform along the axial and in theazimuthal directions in the port.

[0053] It is also an object of the present invention to provide a methodof selecting, or identifying, such hybrid rocket propellants.

[0054] As described in the Background, in a hybrid rocket combustionchamber, liquid oxidizer is converted to gas and caused to flow over thesolid fuel surface. In a reverse hybrid the oxidizer is the solid. Uponignition, a flame sheet is formed above the solid surface and heat fromthe flame melts the solid causing a liquid layer to form. Evaporationfrom the liquid-gas interface produces a continuous flow of fuel gaswhich mixes with oxidizer at the flame sheet thus maintaining thecombustion. At steady state, the regression rate of the melt surface andthe liquid-gas interface are the same and the thickness of the liquidlayer is constant. FIG. 4 shows typical steady state temperature andvelocity profiles in a liquefying hybrid rocket.

[0055] The inventors have discovered, and according to the presentinvention, the liquid layer at the melt surface can be hydrodynamicallyunstable under the mass flux, pressure and temperature conditions whichoccur in a hybrid rocket combustion chamber. This shear-driveninstability leads to wave formation on the liquid-gas interface and asthe waves develop nonlinearly, the displaced liquid-gas interfaceexposed to the high speed flow of gas can breakup, leading to theformation of concentrated pockets of high density fuel and/or fueldroplets which are entrained into the gas stream. The mechanism ofliquid layer instability and entrainment can substantially increase therate of mass transfer from the fuel surface. This situation isillustrated schematically in FIG. 5.

[0056] We have developed a method for solid propellant selection oridentification that takes the mechanism of liquid layer instability andentrainment into account. This method of the present invention has beenused to identify high regression rate solid fuels and to predict theirperformance. It can be applied equally well to solid fuels or oxidizerswhich are collectively referred to as propellants. An important elementof the process is a criterion that determines whether a given solidpropellant is more or less likely to produce entrainment for a given setof combustion chamber conditions.

[0057] Accordingly, the present invention provides for a fuelcomposition suitable for use in hybrid rockets having a fuel componentand an oxidizing component. One of the components flows past the other,and under the heat of combustion (heat transfer from the flame) one ofthe components forms an unstable melt layer with viscosity and surfacetension such that droplets from the melt layer are entrained in theother component thereby increasing the burning rate. The presentinvention can also be used in formulating a fast burning fuel for solidfuel ramjet applications.

[0058] In another aspect of the present invention a propulsion system isprovided. The propulsion system includes a vehicle structure,terminating in a nozzle and having a fuel component within thestructure. One or more combustion chambers are formed within, oralternatively contain, the fuel component. Also provided is an oxidantvessel within the vehicle structure for flowing the oxidant in contactwith the one or more combustion chambers to react with the fuel. Thefuel is selected such that under the heat transfer from the flame, thefuel forms an unstable melt layer with viscosity and surface tensionsuch that droplets of the melted fuel are entrained in the flowingoxidant thereby increasing the burning rate.

[0059] In yet another aspect of the present invention, a combustiblehybrid fuel having a solid fuel component and a flowing oxidizercomponent flowing through one or more ports is provided. The solid fuelforms a liquid layer at the interface between the oxidizer and fuel, andthe liquid layer exhibits entrainment of liquid droplets in the flowingoxidizer at an entrainment rate of${\overset{.}{r}}_{ent} \propto {\frac{\left( {C_{f}P_{d}} \right)^{\alpha}h^{\beta}}{µ^{\gamma}\sigma^{\pi}} \cdot}$

[0060] In still another aspect of the present invention a method ofselecting a propellant that exhibits a desirable regression rate duringcombustion within a port having a gas stream flowing through the port isprovided. The method comprises the steps of:

[0061] for a given port mass flux, G=ρ_(g)U_(g), where ρ_(g) is the portaverage gas density and where U_(g) is the port average gas velocity;and

[0062] for a thickness h of a liquid layer formed on the surface of thefuel;

[0063] wherein the port mass flux value and the thickness satisfy therelationship of

G ^(1.6) h ^(0.6) ≧a _(onset)

[0064] and where a_(onset) is the entrainment onset parameter and isgiven by:$a_{onset} = {1.05 \times 10^{- 2}\left( \frac{\rho_{g}^{1.3}}{\rho_{l}^{0.3}} \right)\frac{1}{\left( {C_{fref}C_{B1}} \right)^{0.8}}\left( \frac{1}{µ_{g}} \right)\sigma \quad µ_{l}^{0.6}\quad {and}}$

[0065] selecting the propellant such that a_(onset) has a value thatpromotes entrainment of droplets from the liquid layer into the gasstream in the port.

BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Additional objects and advantages of the invention will becomeapparent in reading the detailed description of the invention and theclaims and with reference to the figures, in which:

[0067]FIG. 1 is a schematic diagram of a hybrid rocket which may beemployed with the present invention.

[0068]FIG. 2 is a schematic diagram of the combustion configuration in asingle port hybrid rocket motor.

[0069]FIG. 3 is a schematic diagram of a wagon wheel port hybrid rocketmotor.

[0070]FIG. 4 is a schematic diagram illustrating velocity andtemperature profiles in a liquefying hybrid rocket.

[0071]FIG. 5 is a schematic diagram showing entrainment of the meltlayer during combustion according to the present invention.

[0072]FIG. 6 is a graph illustrating melting, vaporization and averagemelt layer temperature of n-paraffins as a function of molecular weightand according to one embodiment of the present invention.

[0073]FIG. 7 is a graph depicting viscosity as a function of themolecular weight for various n-paraffins (normal paraffins) and twohighly crystalline polyethylene waxes.

[0074]FIG. 8 shows the viscosity and surface tension of the melt layeras a function of the molecular weight for various n-paraffins accordingto one embodiment of the present invention.

[0075]FIG. 9 illustrates the presence of entrainment for variousn-paraffins as a function of their molecular weight.

[0076]FIG. 10 is a graph showing regression rates as a function ofoxidizer mass flux for paraffins A and B according to one embodiment ofthe present invention.

[0077]FIG. 11a is a photograph showing the plume from a conventionalPMMA/GOX hybrid rocket systems.

[0078]FIG. 11b is a photograph showing the plume from a paraffin wax(grade B)/GOX hybrid rocket system of the present invention.

[0079]FIGS. 12a and 12 b are schematic cross sectional end views of adouble D port, and circular single port, hybrid rocket motorconfigurations, respectively, according to two embodiments of thepresent invention.

[0080]FIG. 13 is a graph showing the regression rate for paraffin wax Baccording to the present invention, in comparison to the estimatedclassical regression rate of the prior art.

DETAILED DESCRIPTION OF THE INVENTION

[0081] The invention is now described in more detail. The followingterms used throughout the description herein are defined below as:

[0082] a_(h) Liquid layer thickness parameter, m²/sec

[0083] a_(cl) Classical regression rate parameter, m^(2.6)/kg^(0.8)−sec

[0084] a_(onset) Entrainment onset parameter, kg^(1.45)/m^(2.3)−sec

[0085] a_(ent) Entrainment regression rate parameter,m^(2.6)/kg^(0.8)−sec

[0086] B Blowing parameter

[0087] C_(B1) Blowing correction coefficient

[0088] C_(f) Friction coefficient

[0089] C_(fref) Reference friction coefficient

[0090] C_(l) Liquid specific heat, J/kg−K

[0091] C_(S) Solid specific heat, J/kg−K

[0092] G Port average mass flux, kg/m²−sec

[0093] h Melt layer thickness, m

[0094] h_(v) Effective heat of gasification, J/kg

[0095] h_(vcl) Classical effective heat of gasification, J/kg

[0096] L_(m) Latent heat of melting, J/kg

[0097] L_(v) Latent heat of vaporization, J/kg

[0098] L_(grain) Length of the port, m

[0099] M_(wg) Mean molecular weight of the port gas, kg/kmole

[0100] P_(g) Port mean pressure (chamber pressure), N/m² (Pascal)

[0101] P_(d) Dynamic pressure in the port, N/m²

[0102] {dot over (Q)}r Radiative heat flux, J/m²−sec

[0103] Convective heat flux, J/m²−sec

[0104] R_(l) Thermal to radiation thickness ratio

[0105] Re_(z) Reynolds number based on distance along the port

[0106] R_(u) Universal gas constant, J/kmole−K

[0107] {dot over (r)} Surface regression rate, m/sec

[0108] {dot over (r)}_(cl) Local regression rate predicted by classicaltheory, m/sec

[0109] {dot over (r)}_(e) Regression rate component due to entrainment,m/sec

[0110] T_(a) Ambient fuel temperature, K

[0111] T_(g) Port mean temperature, K

[0112] T_(m) Melting temperature, K

[0113] T_(b) Boiling temperature, K

[0114] T_(interface) Liquid-gas interface temperature, K

[0115] T_(solid) Characteristic temperature for the solid, K

[0116] T_(liquid) Characteristic temperature for the liquid, K

[0117] ΔT₁ Temperature difference T_(interface)−T_(m), K

[0118] ΔT₂ Temperature difference T_(m)−T_(a), K

[0119] U_(g) Port average gas velocity, m/sec

[0120] z Axial distance along the port, m

[0121]  Liquid thermal conductivity, J/m−sec−K

[0122] μ_(l) Liquid viscosity, kg/m−sec

[0123] μ_(g) Port mean gas viscosity, kg/m−sec

[0124] τ_(interface) Shear stress at the liquid-gas interface, N/m²

[0125] ρ_(s) Solid density, kg/m³

[0126] ρ_(l) Liquid density, kg/m³

[0127] ρ_(g) Port average gas density, kg/m³

[0128] a Surface tension, N/m

[0129] The theory which underlies the present invention indicates thatpropellant surface tension and especially liquid layer viscosity at thecombustion chamber conditions are the key physical properties thatdetermine whether or not the propellant will entrain.

[0130] The inventors have found that members of the n-alkane (normalalkane) class of hydrocarbons, C_(n)H_(2n+2) which are solid at roomtemperature and having a mean carbon number of n>15, more preferably nis in the range of 15 to 80, with a range of 18 to 40 being mostpreferred, have low surface tension and viscosity at the melt layerconditions typical of hybrid rockets. According to the presentinvention, these fuels are predicted to have high regression rates atoxidizer mass fluxes covering a wide range of hybrid rocketapplications. In addition to the n-alkanes, some isomers of the alkaneseries will also satisfy the entrainment criterion found by theinventors.

[0131] Above a certain molecular weight, entrainment does not occur.This includes polymeric materials which are often used in conventionalhybrid rocket applications. Even though some of these polymers form aliquid layer, it is too viscous for entrainment to occur for the rangeof port mass fluxes encountered in hybrid rockets.

[0132] According to the present invention, the selection procedure isgenerally as follows. The entrainment onset criterion (a_(onset)) isused to estimate the combination of port mass flux given by:

G=ρ _(g) U _(g)  (1)

[0133] and liquid layer thickness, h, required to cause a givenpropellant to entrain. A high regression rate propellant is one thatwill entrain for the range of mass fluxes that are expected to occur inthe given application. A number of fuels including the paraffin waxes,polyethylene waxes, solid organic acids and alkylnapthalenes fall intothis category. A low regression rate propellant is one that, by thiscriterion, would only entrain for mass fluxes in excess of thoseproduced in the given application. In other words, at the port mass fluxthe rocket is designed for, entrainment would not occur. Conventionalhybrid fuels such as high density polyethylene (HDPE) fall into thelatter category and typically burn at the rate predicted by classicalhybrid theory. Thus, a significant advantage the method of the presentinvention is that it can be used to select a propellant that willexhibit a high regression rate tailored to a particular application ormission.

[0134] Propellant Selection Method

[0135] The analysis of liquid layer formation and entrainment wasperformed in three stages. A more detailed description may be found inKarabeyoglu, M. A. “Transient Combustion in Hybrid Rockets”, StanfordUniversity Ph.D. Thesis, August 1998 (reference 2), the entiredescription of which is hereby incorporated by reference. In the firststage, the formation of a melt layer on the solid surface was studied.In the second stage, the linear stability of the melt layer under thestrong shear of a gas flow was examined. The linear stability modelincluded the effect of the vertical motion of liquid at the liquid-solidinterface due to the regression of the fuel slab. Later in the secondstage the linear stability results were linked to the entrainment ofliquid droplets through the use of both experimental results andsemi-empirical relations found in the literature, references [3, 4, 5].In the final stage, classical hybrid theory [1] was further developed toinclude liquid droplet entrainment. It is possible to show that theprimary effect of the entrainment mass transfer is to increase theregression rate of the fuel without increasing the thermochemicallydefined blowing parameter. The implication of this is that the dropletentrainment mechanism does not rely on a reduced heat of gasification ofthe fuel. In the following paragraphs the details of each step of theselection process are described.

[0136] First, an estimation of the melt layer thickness as a function ofregression rate is made. The film thickness formed on a burning slabunder the combined heating of convection and radiation was considered.Physically, the thickness of the liquid layer is determined by theenergy transfer relations both in the solid and also in the liquid. Weare solely interested in the steady-state regression of the fuel slab.For that reason, the regression rate of the liquid-gas interface and thesolid-liquid interface are assumed to be equal and constant. This, ofcourse, implies that the thickness of the melt layer is also constant.For the sake of simplicity we further assumed that the thermophysicalproperties of the material both in the liquid phase and also in thesolid phase are uniform. The effect of convection in the liquid layerwas also ignored. This assumption can be justified for small melt layerthicknesses for which the Reynolds numbers are relatively small (a fewhundred) and the temperature gradients are fairly large.

[0137] In the analysis, the possibility of the penetration of thermalradiation into the slab is considered. Several simplifying assumptionsare introduced in the treatment of radiative heat transfer. First, theradiative flux field is assumed to be one dimensional. The absorbingcharacter of both the liquid and the solid material is assumed to behavelike a gray body; namely the absorption coefficient is independent ofthe frequency of the radiation.

[0138] Under these simplifications, the energy equations in the liquidand solid phases of the slab were used to solve for the thickness of themelt layer formed on the fuel surface. The results indicate that for agiven fuel the melt layer thickness, h, is inversely proportional to thetotal regression rate of the fuel slab. $\begin{matrix}{h = \frac{a_{h}}{\overset{.}{r}}} & (2)\end{matrix}$

[0139] where h is the liquid layer thickness, and {dot over (r)} is thefuel surface regression rate due to the combined effects of vaporizationand entrainment. A complete analysis of the liquid layer has beencarried out. Two limiting cases are of primary interest depending on aparameter, R_(l), which is the ratio of the thermal thickness to theradiative penetration thickness in the liquid layer.

[0140] If R_(l)>>1 the liquid layer is opaque to radiation from theflame and all the radiation is absorbed at the liquid-gas interface. Inthis case $\begin{matrix}{a_{h} = {\left( \frac{\lambda}{\rho_{l}C_{l}} \right){{{Ln}\left( \frac{1 + \frac{L_{m}}{C_{s}\Delta \quad T_{2}} + {\left( \frac{\rho_{l}}{\rho_{s}} \right)\frac{C_{l}\Delta \quad T_{1}}{C_{s}\Delta \quad T_{2}}}}{1 + \frac{L_{m}}{C_{s}\Delta \quad T_{2}}} \right)} \cdot}}} & (3)\end{matrix}$

[0141] Generally, one tries to achieve this condition by preferablyadding a strong absorber such as carbon black to the propellant so thatas much radiation as possible is absorbed in the liquid layer.

[0142] In the limit R_(l)<<1, the absorption of radiation in the liquidlayer is small so that all of the radiative flux is absorbed in thesolid. The thickness parameter, ah, in this limit is given by$\begin{matrix}{a_{h} = {\left( \frac{\lambda}{\rho_{l}C_{l}} \right){{Ln}\left( \frac{1 + \frac{L_{m}}{C_{s}\Delta \quad T_{2}} + {\left( \frac{\rho_{l}}{\rho_{s}} \right)\frac{C_{l}\Delta \quad T_{1}}{C_{s}\Delta \quad T_{2}}} - {\frac{h_{v}}{C_{s}\Delta \quad T_{2}}\left( \frac{{\overset{.}{Q}}_{r}/\overset{.}{Q_{c}}}{1 + {{\overset{.}{Q}}_{r}/\overset{.}{Q_{c}}}} \right)}}{1 + \frac{L_{m}}{C_{s}\Delta \quad T_{2}} - {\frac{h_{v}}{C_{s}\Delta \quad T_{2}}\left( \frac{{\overset{.}{Q}}_{r}/\overset{.}{Q_{c}}}{1 + {{\overset{.}{Q}}_{r}/\overset{.}{Q_{c}}}} \right)}} \right)}}} & (4)\end{matrix}$

[0143] where the characteristic temperatures differences are

ΔT ₁ =T _(interface) −T _(m) ; ΔT ₂ =T _(m) −T _(a).  (5)

[0144] The heat of gasification averaged over all the mass leaving thefuel surface is $\begin{matrix}{h_{v} = {{C_{s}\Delta \quad T_{2}} + L_{m} + {\left( \frac{\rho_{l}}{\rho_{s}} \right)C_{l}\Delta \quad T_{1}} + {L_{v}\left( \frac{{\overset{.}{r}}_{v}}{\overset{.}{r}} \right)}}} & (6)\end{matrix}$

[0145] where ({dot over (r)}_(v)/{dot over (r)}) is the fractional massthat vaporizes. The classical heat of gasification in the absence ofdroplet entrainment is $\begin{matrix}{h_{vcl} = {{C_{s}\Delta \quad T_{2}} + L_{m} + {\left( \frac{\rho_{l}}{\rho_{s}} \right)C_{l}\Delta \quad T_{1}} + {L_{v} \cdot}}} & (7)\end{matrix}$

[0146] The heat of gasification is the total heat required to transformthe fuel from the solid state at its ambient temperature, T_(a), to thegas state at the average liquid-gas interface temperature,T_(interface). The factor ({dot over (r)}_(v)/{dot over (r)}) appearingin equation (6) accounts for the fact that a given parcel of fuel masscan reach the free stream through two routes; one route beingvaporization and involving the usual four steps of solid heating,melting, liquid heating and evaporation; and the other route beingentrainment and involving the first three steps but not requiringevaporation. The droplets do eventually evaporate as they convect alongthe port and interact with the flame but this process does notcontribute to the heat or mass balance at the liquid-gas interface.

[0147] The average temperature at the liquid-gas interface,T_(interface), must be estimated. As a first approximation one couldtake the boiling temperature of the liquid at standard conditions.Evaporation reduces this temperature slightly below boiling. Elevatedvapor partial pressure tends to increase the boiling temperature butentrainment tends to decrease the temperature until, at high entrainmentrates, the liquid layer thickness becomes small and the liquid-gasinterface temperature approaches the melt temperature (a quantity whichis insensitive to pressure). For simplicity, a reasonable estimate whichis valid over the range of conditions of interest is used. We let

T _(interface) =T _(m)+0.8(T _(b) −T _(m))  (8)

[0148] where T_(b) is taken to be the boiling temperature of the liquidfuel at one atmosphere. The quantity {dot over (Q)}_(r)/{dot over(Q)}_(c) is the ratio of radiative to convective heat transfer to theliquid-gas interface and must be estimated. A reasonable range, validover the conditions found in hybrid rockets is {dot over (Q)}_(r)/{dotover (Q)}_(c)<0.2. Fortunately, as long as {dot over (Q)}_(r)/{dot over(Q)}_(c) is small, the calculated value of the liquid layer thickness isnot sensitive to errors in the quantities which appear in the logarithm.But notice that there is a critical value of {dot over (Q)}_(r)/{dotover (Q)}_(c) when the denominator in the logarithm in (4) becomes zero.This corresponds to a condition where there is no steady state solutionto the melting problem and the thickness of the liquid layer continuesto grow toward a state where the entire block of fuel is being heated tothe melting point by radiation.

[0149] The thermal diffusivity factor outside the logarithm in equation(4) is known reasonably well as a function of temperature.

[0150] A complicating factor in this picture is that the port meanpressure may exceed the critical pressure of the liquid. Thermodynamicequilibrium theory indicates that above the critical pressure thesurface distinguishing liquid and gas is not precisely defined and thedensity varies continuously from the melt layer to the gas. In fact themelt layer in a hybrid rocket may not be in an equilibrium state and thedetailed physics of the liquid-gas interface is not well understood.Thus in this document the word “droplet” has a generalized meaningreferring to any parcel of propellant at or close to the density of themelt layer and the phrase “liquid-gas interface” refers to a transitionlayer from liquid to gas that may not have a distinct surface althoughthe surface of maximum density gradient is often used as a reference.Nevertheless, one can assume that even above the critical pressure, thebasic mechanism of instability of the melt layer and entrainment ofparcels of propellant at or close to the melt density still occurs.Moreover, one can assume that a propellant that entrains undersubcritical conditions will also entrain when the port mean pressureexceeds the critical pressure of the propellant.

[0151] Second, an estimation of the friction coefficient is made. Thefriction coefficient at the liquid-gas interface is approximately$\begin{matrix}{C_{f} = {\frac{\tau_{interface}}{\frac{1}{2}\rho_{g}U_{g}} = {{C_{fref}\left( {R\quad e_{z}} \right)}^{- 0.2}C_{B1}}}} & (9)\end{matrix}$

[0152] where τ_(interface) is the shear stress at the gas-liquidinterface. The reference shear stress is taken to be C_(fref)=0.03. TheReynolds number based on the distance, z, along the port is$\begin{matrix}{{R\quad e_{z}} = {\frac{\rho_{g}U_{g}^{z}}{µ_{g}} = {\frac{G\quad z}{µ_{g}} \cdot}}} & (10)\end{matrix}$

[0153] The factor $\begin{matrix}{C_{B1} = \left( \frac{2}{2 + {1.25B^{0.75}}} \right)} & (11)\end{matrix}$

[0154] corrects (reduces) the surface friction for the effect of theevaporative mass transfer from the surface. This is a new correctionfactor which we have developed which is valid for 0<B<15. The blowingparameter, B, is related to conditions at the flame sheet which aredifficult to determine, however values between B=4 and B=10 are typical.In the calculations presented here we use B=6.

[0155] Third, an estimation of the classical propellant regression rate(without entrainment) is made. Classical hybrid theory describes theregression rate of hybrid fuels in the absence of entrainment. Thewidely accepted formula due to Marxman et al. (reference [1]) is$\begin{matrix}{{\overset{.}{r}}_{cl} = {C_{f}{B\left( {1 + \frac{{\overset{.}{Q}}_{r}}{{\overset{.}{Q}}_{c}}} \right)}{\left( \frac{G}{\rho_{s}} \right).}}} & (12)\end{matrix}$

[0156] When the expression for the friction coefficient is inserted, theresult is

{dot over (r)} _(cl) =a _(cl) G ^(0.8).  (13)

[0157] The factor a_(cl) is, $\begin{matrix}{a_{cl} = {{C_{fref}\left( \frac{2\quad \mu_{g}}{L} \right)}^{0.2}\quad {C_{B1}\left( {1 + \frac{{\overset{.}{Q}}_{r}}{{\overset{.}{Q}}_{c}}} \right)}\left( \frac{B}{\rho_{s}} \right)}} & (14)\end{matrix}$

[0158] with units m^(2.6)/(kg^(0.8)−sec^(0.2)). The equation (12) is alocal relationship which depends weakly on the axial position in theport. Here and throughout we use the convention that the regressionrates are evaluated at the midpoint of the port, i.e. at z=L/2.

[0159] Fourth, the entrainment onset criterion is developed. Theinstability of the melt layer needs to be related to the entrainment ofliquid droplets into the gas stream. To this end, we investigated thelinear stability of the melt layer formed on the solid fuel. This isshown in further detail in “Transient Combustion in Hybrid Rockets”,which is incorporated by reference. This film is subjected to shear bythe gas flow in the port and is also subjected to strong blowing due tothe regression of the fuel surface. The large shear forces exerted bythe high speed gas stream flowing through the port generates instabilitywaves at the liquid-gas interface. A rigorous treatment of theentrainment problem requires an investigation of the nonlineardevelopment of the instability waves and break-off of droplets asdepicted in FIG. 5. The complete physics of this process is extremelycomplex. To address this difficulty we developed empirical relations forthe droplet entrainment mechanism by using experimental data togetherwith the linear stability results presented in “Transient Combustion inHybrid Rockets”.

[0160] Work on entrainment is reported in Reference [3], the descriptionof which is hereby incorporated by reference. In this study, theentrainment rates from thin films of various liquids (including somehydrocarbons such as RP-1 (kerosene) and methanol) under strong shearinggas flow were measured. The experiments were performed in a wind tunneland some tests were executed with hot gas flow.

[0161] The inventors have determined some important factors regardingentrainment mass transfer as follows:

[0162] if the mass flux in the port is less than a critical value thereis no entrainment mass transfer from the film; and

[0163] the general empirical expression for the entrainment rate ofliquid droplets (the entrainment regression rate) in terms of therelevant properties of the hybrid motor can be written as:$\begin{matrix}{{\overset{.}{r}}_{e} \propto {\frac{\left( {C_{f}P_{d}} \right)^{\alpha}h^{\beta}}{\sigma^{\gamma}\mu_{l}^{\delta}}.}} & (15)\end{matrix}$

[0164] where α is approximately 1.5, β is approximately 2.0 and γ and δare approximately 1.0. Here P_(d)=(½)ρ_(g) ^(U) _(g) ² is the dynamicpressure of the gas flow in the port. The powers of each parameteraffecting the entrainment regression rate are positive, empiricallydetermined quantities. In general, it can be stated that the entrainmentincreases with increasing port dynamic pressure and melt layer thicknessand decreases with increasing viscosity and surface tension. Thisexpression has central importance in determining how fast a selectedfuel will burn.

[0165] A useful criterion for the onset of entrainment must account fortwo basic effects. First, at a given mass flux a thick liquid layer ismore unstable and therefore more likely to entrain than a thin layer.Second, for a given liquid layer thickness a higher free stream gas massflux is more likely to entrain than a lower mass flux.

[0166] Following reference [5] the fundamental criterion for the onsetof entrainment is

G ^(1.6) h ^(0.6) ≧a _(onset)  (16)

[0167] where the factor a_(onset) is, $\begin{matrix}{\alpha_{onset} = {1.05 \times 10^{- 2}\left( \frac{\rho_{g}^{1.3}}{\rho_{l}^{0.3}} \right)\quad \frac{1}{\left( {C_{fref}C_{B1}} \right)^{0.8}}\left( \frac{1}{\mu_{g}} \right)\sigma \quad {\mu_{l}^{0.6}.}}} & (17)\end{matrix}$

[0168] The quantity, a_(onset), is computed for a given fuel. If thecomputed value a_(onset) is below a critical range, then the fuel islikely to entrain. According to the present invention, a_(onset) isselected such that a_(onset) has a value that promotes entrainment ofdroplets from the melt layer. Preferably, a_(onset) is equal to or lessthan approximately 0.9, and more preferably a_(onset) is equal to orless than 0.4. We recommend the following ranges: $\begin{matrix}{\left. {0.4 \leq \begin{matrix}{a_{onset} < 0.4} & {{entrainment}\quad {will}\quad {occur}} \\{a_{onset} \leq 0.9} & {{entrainment}\quad {is}\quad {likely}} \\{a_{onset} > 0.9} & {{entrainment}\quad {is}\quad {unlikely}}\end{matrix}} \right\}.} & (18)\end{matrix}$

[0169] The units of a_(onset) are kg^(1.6)/(m^(2.6)−sec^(1.6)) It isimportant to recognize that several of the quantities appearing inequation (17) vary relatively little from one propellant to another. Thefactor, ρ_(l) ^(0.3), is fairly close to one over a wide range of liquiddensities. For the range of blowing factors between 4 and 10, thecoefficient, C_(B1), is between approximately 0.2 and 0.4.

[0170] The gas density and viscosity make α_(onset) depend on the portmean temperature and pressure since $\begin{matrix}{{\frac{\rho_{g}^{1.3}}{\mu_{g}} \propto \frac{P_{g}^{1.3}}{T_{g}^{2.05}}},} & (19)\end{matrix}$

[0171] where the ideal gas law P_(g)=(ρ_(g)R_(u)T_(g))/M_(wg) and gasviscosity-temperature relation μ_(g)∝T_(g) ^(0.75) have been used. Forhydrocarbon fuels, the port mean temperature varies relatively littleover the range of applications so the main sensitivity is to the portmean pressure although the effect is not as strong as P_(g) ^(1.3) sinceas the pressure increases the temperature of the liquid-gas interfaceincreases also, tending to partially mitigate the increase in a_(onset)due to pressure.

[0172] At port mean pressures exceeding the critical pressure of thecandidate propellant, the surface tension goes to zero and aquantitative analysis of entrainment must account for the increasinglydiffusive nature of the mass transfer from the solid surface. One canexpect that the central role of the viscosity of the melt layerindicated by equation (17) for subcritical conditions will continue tobe dominant under supercritical conditions. Thus the onset criteriongiven by equation (17) is a formalism for identifying propellants whichproduce high entrainment under subcritical conditions with theunderstanding that they will also entrain when the port mean pressureexceeds the critical pressure of the material. For this reason, thevalues for a_(onset) quoted here are all for a standard referencepressure of P_(g)=10 atm, and thus a_(onset) may vary at differentreference pressures.

[0173] The factor, σμ_(l) ^(0.6), in a_(onset) indicates the importantrole of the surface tension and the viscosity, especially the viscosity,in determining whether a propellant will entrain. For most liquidhydrocarbons, the surface tension is in the range of 5 to 30 milliN/m.Thus, while the surface tension variation from one material to anotheris moderate, the viscosity varies widely. For example, the viscosity ofhigh density polyethylene (HDPE) is a factor of 10⁴ larger than theviscosity of paraffin at typical melt layer temperatures.

[0174] A fuel that, at the classical regression rate corresponding to agiven mass flux would produce a liquid layer thickness exceeding theonset criterion, is a fuel which is likely to entrain and is therefore agood candidate for a high regression rate fuel. We can use this idea toestimate the port mass flux above which entrainment should occur. Let

h _(cl) ≧h _(onset).  (20)

[0175] Using equations (2), (13) and (16), to express equation (20) as$\begin{matrix}{\frac{a_{h}}{a_{cl}G^{0.8}} \geq {\left( \frac{a_{onset}}{G^{1.44}} \right)^{\frac{1}{0.6}}.}} & (21)\end{matrix}$

[0176] The port mass flux required to cause the onset of entrainment fora given fuel is estimated as $\begin{matrix}{G_{onset} = {\left( \frac{a_{cl}}{a_{h}} \right)^{\frac{0.6}{1.12}}{\left( a_{onset} \right)^{\frac{1}{1.12}}.}}} & (22)\end{matrix}$

[0177] Note that this is a conservative (high) estimate of the onsetport mass flux since it uses a thickness based on the classicalregression rate.

[0178] High Regression Rate Fuels

[0179] Conventional hybrid fuels are all polymeric materials. Theburning surface physics and chemistry of these materials are fairlycomplicated. Some of these fuels form a char layer whereas some form aliquid melt layer. Due to the large size of the long chain molecules inconventional liquefying polymeric fuels (even after some partialpyrolysis), the liquid layers formed on the fuel surface during theburning process have extremely high viscosity and surface tension. Evenunder the very strong shear forces exerted by the gas flowing throughthe port, these viscous liquid films are stable and entrainment ofdroplets into the gas stream does not occur.

[0180] On the contrary, according to the present invention, it isdiscovered that there are several classes of non-polymeric solidmaterials that form a liquid layer with low enough viscosity and surfacetension such that the entrainment of liquid droplets does occur. Thisprovides an important additional mechanism by which mass can betransferred from the solid fuel to the gas stream. We have found boththeoretically and experimentally that the mechanism of liquid layerformation and droplet entrainment can increase the burning rate ofhybrid fuels by two to five or more times the burning rate of classicalhybrid fuels at identical operating conditions.

[0181] Application to N-Alkanes

[0182] We applied the propellant identification process to severalgroups of organic compounds that are in solid phase under ambientconditions. The first and possibly the most significant group from apractical point of view is the series of n-paraffins ranging fromMethane (n=1) all the way up to High Density Polyethylene (HDPE) polymer(n=14, 000). Compounds suitable according to the present inventioninclude the n-alkane class of hydrocarbons of the formula C_(n)H_(2n+2)which are solid at room temperature and have a mean carbon number ofn≧15, more preferably n is in the range of about 15-80, with a range ofabout 18 to 40 being most preferred and isomers of said alkane class ofhydrocarbons. Also, mixtures of various compounds in the series aresuitable. For this group important material properties such as viscositycan be expressed as a function of the molecular weight and thetemperature. The melting, vaporization and average melt temperatures ofthe n-paraffins as functions of the molecular weight are shown in FIG.6. Data points for the melting temperatures of three polyethylene waxesare included in FIG. 6. Note that all three temperatures increaserapidly in the small molecular weight region, whereas in the largemolecular weight region they asymptote to a constant value. For largemolecules the upper temperature limit is dictated by pyrolysis ratherthan vaporization, since the large molecules will tend to break upbefore the vaporization occurs. Note that the pyrolysis temperature forthe high density polyethylene polymer is about 405 C, whereas themelting temperature limit corresponding to the melting temperature ofthe infinite molecular weight 100% crystalline polyethylene polymer is141 C.

[0183] As discussed previously the most important parameters of the meltlayer that determine the entrainment (and thus the total burning rate ofa prospective fuel) are the melt viscosity at an average temperaturebetween the melting temperature and the liquid-gas interfacetemperature, and the surface tension at the liquid-gas interfacetemperature. The plot of viscosity as function of the molecular weightof the normal hydrocarbons for three different temperatures are shown inFIG. 7. FIG. 7 shows a linear variation of viscosity with the molecularweight as expected in this low molecular weight regime. Two additionaldata points for two highly crystalline polyethylene waxes (4040/R7 and4040/R9 of Marcus Oil & Chemical Corporation) are also included in theplot. This specific polyethylene wax is composed of highly linearmolecules and its viscosity can be predicted by the extrapolation of thecurve obtained for the n-paraffins. Although the figure shows asignificant increase of viscosity with the molecular weight at aconstant temperature, the melt layer viscosity actually only increasesslightly due to the increase in the melt layer temperature. Thisimportant fact is presented in FIG. 8 which shows the reduced molecularweight dependence of the melt layer viscosity evaluated at the meanbetween melting and vaporization temperatures. Note that the viscosityvalues are normalized with respect to the n-pentane melt viscosity.However, this temperature effect can only be realized for relativelysmall molecular weights (i.e. paraffin waxes) since the temperatureincrease is quite small above a certain molecular weight.

[0184] Similar arguments hold for the surface tension. Even though thesurface tension of the linear hydrocarbon series increases linearly withincreasing molecular weight at a constant temperature, melt layersurface tension actually decreases with increasing molecular weight asshown in FIG. 8. This effect, which can only be realized for relativelysmall molecular weights, is also due to the increased melt layer surfacetemperatures with increasing molecular weight. These observations on themelt viscosity and surface tension indicate that moderate molecularweight, normal alkanes (i.e. paraffin waxes) will generate entrainmentrates that are several times the regression rates of classical polymerichybrid fuels. The combined effect of the increase in viscosity anddecrease in surface tension is to modestly increase entrainment withincreasing molecular weight in this range.

[0185] It is interesting to note that high density polyethylene (HDPE)polymer is also a member of this linear molecule family in the very highmolecular weight extreme (˜200,000 kg/kmole). The melt viscosity of thehigh density polyethylene is estimated at an average temperature betweenthe melting point (135 C) and the pyrolysis temperature (405 C) with useof a technique presented in reference [6]. Note that a simpleextrapolation cannot be used to determine the melt viscosity of theseliquids with large molecules since above a critical value of themolecular weight, the linear variation of viscosity with molecularweight does not hold. The estimated viscosity value for HDPE is 20Pascal-sec which is 4 orders of magnitude larger than the melt viscosityof paraffin wax or the viscosity of liquid pentane. This explains thelow regression rates (i.e. no entrainment mass transfer) observed formelting polymeric fuels such as high density polyethylene.

[0186]FIG. 9 illustrates a qualitative schematic of the overall picturefor n-paraffins ranging from the smallest molecular mass (methane) toHDPE polymer. Note that materials at both ends of the spectrum have beentried as hybrid fuels. Both extremes have significant deficiencies,namely the high molecular weight HDPE polymer burns slowly and the fastburning low molecular weight compounds are solid only under cryogenicconditions, reference [10]. It is remarkable that the non-cryogenicmaterials in the intermediate molecular mass region (potentially optimumfor hybrid applications) such as paraffin and PE waxes have notpreviously been tried as hybrid rocket fuels.

[0187] First, we carried out a theoretical study of a specific highmelting point (67 C) paraffin wax. We estimated the material properties(an average melt viscosity of 0.65 milliPascals-sec and surface tensionof 7.1 milliNewtons/m) of this wax (which would have an approximateaverage carbon number of 31) and applied the theory to show that liquidentrainment levels for this wax were quite high. The theory indicatedthat a paraffin wax with these properties was likely to burn severaltimes, in particular 3 to 5 times, faster than conventional hybridfuels.

[0188] Comparison Between Paraffin and Several Conventional Hybrid Fuels

[0189] Preliminary laboratory tests with Plexiglas (PMMA), high densitypolyethylene, HDPE a high molecular weight PE wax and two grades ofparaffin wax with melting points of 61 C and 67 C, hereafter referred toas paraffin grades A and B respectively were made. The wax was melted ina melt pot under a controlled pot temperature of 90 C and mixed withcarbon black (<1% mass fraction) with an average particle size of 18 nm.The mixture was molded in the motor case at room temperature andatmospheric pressure. The PE wax grains were machined with theappropriate port diameter to fit the motor case.

[0190] The conditions and results for these preliminary experiments areshown in Table 1 below. The regression rate values shown in Table 1 arecalculated both by geometrical measurement of the change in the portdimensions and also by measuring the weight reduction in the grainduring the experiment. Both methods yield similar values for theregression rate. TABLE 1 Propellant Paraffin Paraffin tested HDPE PMMAPE wax wax A wax B Initial port 1.27 1.27 1.27 1.27 1.27 diameter cmPort 30.5 30.5 18 18 18 length cm Bum 5 5 5 5 5 time sec Oxidizer 8.368.36 8.36 8.36 8.36 flow rate gm/sec Regression 0.025 0.028 0.036 0.1140.100 rate cm/sec

[0191] Test results for the high molecular weight PE wax grains showed a30% increase in regression relative to Plexiglas at identical operatingconditions. As indicated by the theory this high molecular weight waxdoes form a melt layer, but does not entrain a significant amount ofliquid droplets because the viscosity of the melt layer is too high. Theregression rates for the paraffin grade B grains were found to beapproximately 3.6 times larger than the regression rates measured forthe Plexiglas material tested under identical operating conditions.After the burn, the paraffin grains were undamaged and the burningsurface was smooth and very uniform in both the azimuthal and axialdirections. It was also found that the lower molecular weight wax, gradeA, burned slightly faster and the regression rate was determined to beapproximately 4.1 times larger than the regression rate of Plexiglas(polymethyl methacrylate-PMMA).

[0192] The plume length and diameter was observed to be several timeslarger for paraffin than for the other fuels even though the oxidizermass flux was the same for all runs. The photos in FIGS. 11a and 11 bprovide a comparison between the plumes for PMMA and paraffin grade B.

[0193] The space-time averaged regression rates obtained from multipletests for wax grades A and B with an initial port diameter of 2.54 cmare plotted as a function of the average oxidizer flux in the port andare shown in FIG. 10.

[0194] A partial list of suggested additives that could be used in apractical fuel formulation based on the paraffin wax would includeCarbon Black (0.2-1% by weight), some PE wax (or other kinds of highmolecular weight synthetic waxes) to provide desired mechanicalproperties and thermal stability and possibly some density increasingagents such as Escorez. The role of carbon black (or an alternativematerial with high optical absorptivity) is to improve the radiativeabsorptivity of the fuel to insure that most of the radiation from theflame is absorbed at the fuel surface. This is important since paraffinwax alone may be heated in bulk by the penetration of radiation from theflame zone resulting in uncontrolled burning and possible sloughing ofthe fuel. Additionally, reinforcing or stiffening agents may be added toprovide mechanical rigidity.

[0195] The grade of paraffin and the concentration of additives can beadjusted to obtain the combination of burning rate and mechanicalproperties that suits the mission under consideration. For example, formissions requiring low mass flow generation rates and high mechanicalloading conditions, a high molecular weight paraffin could be selectedand/or a significant concentration of PE wax could be added.

[0196] The fuel formulation can be varied spatially in the fuel grain inorder to passively control the fuel mass flow generation rate as afunction of time. This technique would allow one to design hybridrockets with a desired thrust history and with little or no compromisein the specific impulse.

[0197] Other Organic Compounds

[0198] We have identified two other families of compounds that are goodcandidates for fast burning hybrid fuels. These are thealkhylnaphthalenes (including straight naphthalene) anthracene andcertain organic acids. The organic acids finding use in the presentinvention include organic acids having the general formula ofCH₃(CH₂)nCOOH, where n is in the range of 8 to 25, and mixtures thereof.Naphthalene C₁₀H₈ which is a crystalline material with a melting pointof 354 K, is determined to possess melt layer properties that wouldallow for reasonable entrainment. Some of the other organic compoundsthat belong to the family of Alkhylnaphthalenes with lower meltingpoints and slightly higher viscosity compared to Naphthalene are2,6-Methylnaphthalene, 1-Phenylnaphthalene, 2,6-Diethyl-naphthalene and2,6 Diisopropylnaphthalene [7]. All of these materials have high soliddensities typically in the 1100-1200 kg/m³ range which is a verydesirable property. One other close relative of Naphthalene which isalso a good candidate as a high burning rate material is AnthraceneC₁₄H₁₀. This promising material has a very high melting point (489 K),very low melt viscosity and surface tension and high solid density, 1300kg/m³.

[0199] The other group of materials is the organic acids. First weconsider the series of normal acids CH₃(CH₂)_(n)COOH with varyingmolecular weights. Similar to the paraffins, the melting temperature ofthe material increases with increasing number of the CH₂ group in themolecule. For example, for n=9 (n-nonanoic acid) the melting temperatureis 286 K, whereas, for n 20 (n-eicosanic acid) melting occurs at 348 K.For this series, in the range of high enough melting temperatures, themelt viscosity and surface tension levels are moderate and the expectedentrainment rates would be moderate compared to the level predicted andobserved for paraffin waxes. This series may be useful as additives tohigher entrainment rate fuel materials described previously. Oneimportant member of this series is Stearic acid n=18 which is a widelyused additive for the paraffin waxes. It is known that Stearic acidmodifies the mechanical properties of the paraffin wax. Another acidwhich is not a member of the normal acid family is Glutaric acid C₅H₈O₄.This particular acid has a melting point at 407 K and a solid density of1427 kg/m³. It possesses a moderate to low melt viscosity and surfacetension.

[0200] The above listed chemicals is not exhaustive, and is not anattempt to give a complete list of compounds that would be used as highburning rate fuel materials in hybrid rockets. The few examplesdiscussed above is only a small fraction of the set of possiblefast-burning fuel materials which would satisfy the teaching andcriteria of the present invention.

[0201] System Implications of High Burning Rate

[0202] The impact of high burning rate on the design of a hybrid rocketvehicle is significant. If the burning rate is 3 to 5 times larger thanthe conventional hybrid fuels, a complicated wagon wheel design can, inmany applications, be replaced with either a simplified Double D designas shown in FIG. 12a or even with a single port grain configuration asshown in FIG. 12b. The overall vehicle surface area is reduced and thevehicle volume would also be smaller due to better volumetric loading ofthe fuel. Of particular advantage, all these factors contribute to asmaller, lighter vehicle for a given mission and specified payload.Apart from the weight benefits, the manufacturing costs would besignificantly reduced due to the simple grain design and use ofrelatively inexpensive fuels. The simpler design would lend itself to amore reliable system. In short, a hybrid utilizing a fast burning fuelaccording to the present invention is economically superior to aconventional hybrid or, for that matter, to a conventional liquid orsolid system. The fast burning hybrid should be able to provideperformance which is comparable to or better than a conventional solidor liquid system.

[0203] One other issue that deserves to be mentioned is aft oxidizerinjection. Although oxidizer injection in the post-combustion chamberyields marginal advantages for conventional hybrids which operate in amulti-port configuration with a relatively thin web, it promises agreater benefit for the fast burning hybrid. Aft-end injection makes apartially controllable system (thrust or Isp, not both) a fullycontrollable one. Any given thrust and Isp schedule can be obtained bysetting the main and aft-end oxidizer injection schedules. This makesthe fast burning hybrid propulsion system comparable to liquid systemsin terms of controllability.

[0204] In another embodiment of the present invention, the method ofselecting a high regression rate fuel is provided in stepwise fashion asfollows:

[0205] 1) Specify the length of the fuel grain, L_(grain) and portgeometry.

[0206] 2) Estimate or measure the thermochemical properties of thecandidate material including the melting temperature, T_(m), the normalboiling temperature, T_(b), latent heat of fusion, L_(m) and latent heatof vaporization, L_(v).

[0207] 3) Estimate the temperature of the liquid-gas interface using

T _(interface) =T _(m)+0.8(T _(b) −T _(m))

[0208] Here T_(b) is the normal boiling temperature of the candidatematerial. The use of normal boiling point to evaluate the surfacetemperature implicitly assumes a surface vapor partial pressure ofapproximately 1 atm. The surface temperature is reduced from itsvaporization value using equation (8) to account for the effect ofentrainment which decreases the effective surface temperature.

[0209] 4) Calculate the characteristic solid temperature as$T_{solid} = \frac{T_{m} + T_{a}}{2}$

[0210] Calculate the characteristic melt layer temperature as$T_{liquid} = \frac{T_{m} + T_{interface}}{2}$

[0211] 5) Evaluate the properties of the solid at T_(solid) includingC_(s)(T_(solid))

[0212] 6) Evaluate liquid layer properties other than surface tension atT_(liquid) including C_(l)(T_(liquid)), ρ_(l)(T_(liquid)) andμ_(l)(T_(liquid))

[0213] 7) Evaluate the surface tension, σ, at T_(interface).

[0214] 8) Calculate the entrainment onset parameter$a_{onset} = {1.05 \times 10^{- 2}\left( \frac{\rho_{g}^{1.3}}{\rho_{l}^{0.3}} \right)\frac{1}{\left( {C_{fref}C_{B1}} \right)^{0.8}}\left( \frac{1}{\mu_{g}} \right)\sigma \quad {\mu_{l}^{0.6}.}}$

[0215] The gas density is calculated from the ideal gas law.$\rho_{g} = \frac{P_{g}M_{wg}}{R_{u}T_{g}}$

[0216] where the universal gas constant is R_(u)=8314 J/kmole−K and theunits of P_(g) are N/m². The following values are suggested forpreliminary calculations:

M _(wg)30 kg/kmole; T _(g)=1500K; P _(g)=10 atm

μ_(g)=6.6×10⁻⁵ kg/m−sec; C _(fref)=0.03; B=6

[0217] 9) Entrainment Criterion—Use the following ranges.

a _(onset)<0.4 entrainment will occur

0.4<a _(onset)<0.9 entrainment is likely

a _(onset)>0.9 entrainment is unlikely

[0218] The units of a_(onset) are kg^(1.6)/(m^(2.6)−sec^(1.6))

[0219] 10) Determine a_(cl) and a_(h) and estimate the port mass fluxrequired for entrainment at P_(g)=10 atm.$\left( G_{onset} \right)_{P_{g} = 10} = {\left( \frac{a_{cl}}{a_{h}} \right)^{\frac{0.6}{1.12}}\left( a_{onset} \right)^{\frac{1}{1.12}}}$

[0220] The entrainment onset mass flux at the port mean pressure of thegiven application is determined from$\frac{G_{onset}}{\left( G_{onset} \right)_{P_{g} = 10}} = \left( \frac{P_{g}}{10} \right)^{\frac{1.3}{1.12}}$

[0221] If G_(onset) is below the port mass flux expected in the givenapplication then regression rate enhancement due to entrainment can beexpected to occur.

EXAMPLES

[0222] The following examples are offered for illustration purposesonly, and is not intended to limit the present invention in any way.

Paraffin Fuel Example

[0223] Propellant Selection Process

[0224] 1) We carried out a series of experiments on paraffin grade Bwith an initial port diameter of 2.54 cm. The length of the fuel grainin these experiments was L_(grain)=0.18 m and the port mean pressure wasapproximately P_(g)=10 atm.

[0225] 2) The following parameters are estimated for the selected gradeof wax (melting point 66.6C.

T _(m)339.6 K; T _(boiling)=727.4 K (1 atm)

L _(m)=167.2×10³ J/kg; L _(v)=163.5×10³ J/kg

[0226] 2) The liquid-gas interface temperature is calculated to be

T _(interface)=649.8 K.

[0227] 3) The characteristic temperatures of the melt layer and thesolid are

T _(solid)=319.8 K; T _(liquid)=494.7 K

[0228] where the ambient temperature of the fuel is taken as

T _(a)=300.0 K.

[0229] 4) Solid state properties evaluated at the characteristictemperature are

C _(s)=2.03×10³ J/kg−K; ρ _(s)=930 kg/m ³.

[0230] 5) Liquid state properties evaluated at the characteristictemperature are

C _(l)=2.92×10³ J/kg−K; ρ _(l)=654.4 kg/m ³

μ_(l)=0.65×10⁻³ kg/m−sec; λ _(l)0.12 J/m−K−sec

[0231] 6) Estimate the surface tension

σ=7.1×10⁻³ N/m

[0232] 7) We use the following suggested values:

M _(wg)=30 kg/kmole; T _(g)=1500K; B=6

μ_(g)=6.6×10⁻⁵ kg/m−sec; C _(fref)=0.03

[0233] 8) The entrainment onset parameter is calculated to be

a _(onset)=0.276 kg ^(1.6)/(m ^(2.6) −sec ^(1.6))

[0234] Since a_(onset)≦0.4 the selected grade of wax will entrainvigorously.

[0235] 9) The entrainment onset mass flux is,

G _(onset)=5.2 kg/(m ² −sec)

[0236] which is low compared to corrected port mass fluxes encounteredin hybrid applications. When the onset mass flux is corrected to a highport mean pressure of 100 atmospheres, the value of G_(onset) increasesto 69.4 kg/(m²−sec) which is still well below the range of mass fluxesencountered in applications.

[0237] Regression Rate Measurements for Paraffin (Melting Point 67C)

[0238] The paraffin data for the grade B wax are presented in FIG. 13 asa function of the total mass flux in the port. For B=6, L=0.18 m and{dot over (Q)}_(r)/{dot over (Q)}_(c)=0.1 the classical regression ratecoefficient is estimated to be

a _(cl)=1.48×10⁻⁵ m ^(2.6) /kg ^(0.8) −sec ^(0.2).

[0239] The classical regression rate curve is plotted in FIG. 13 forcomparison with the data. Over the range of mass fluxes studied, theregression rate measured for paraffin is approximately 3.4 times therate predicted from classical theory.

[0240] Entraining Onset Examples for Other Organic Compounds

[0241] The entrainment onset parameter has been determined for a varietyof organic compounds at P_(g)=10 atm and with B=6. The results are shownin table 2. TABLE 2 1-Phenyl 2,6 Diethyl Stearic Glutaric Naphthalenenaphthalene naphthalene Anthracene acid acid Paraffin B Material C₁₀H₈C₁₆H₁₂ C₁₄H₁₆ C₁₄H₁₀ C₁₈H₃₆O₂ C₅H₈O₄ C₃₁H₆₄ T_(m), K 353.43 318.15322.15 489.25 342.75 370.65 339.6 T_(boiling), 491.14 607.15 576.00615.18 648.35 576.15 727.4 K ρ_(l), 936.7 987.5 921.94 939.72 764.121136.2 654.4 kg/m³ ρ_(s), 1049 1096 1168 1233 1010 1429 930 kg/m³ μ_(l),0.54 1.00 0.81 0.47 1.30 0.68 0.65 milliPa-sec σ, 21.7 20.2 21.0 19.611.1 12.5 7.1 milliN/m $\begin{matrix}{a_{onset},} \\\frac{{kg}^{1.6}}{m^{2.6} - \sec^{1.6}}\end{matrix}\quad$

0.678 0.899 0.841 0.563 0.625 0.424 0.276

[0242] The parameter values for paraffin are shown for comparison. Eachof the materials listed above is likely to entrain in a hybrid motorapplication with the possible exception of 1-phenyl naphthalene. Notethat they are relatively dense compared to paraffin and can be mixedwith paraffin to increase fuel density without sacrificing muchentrainment. Notice also that, of all the compounds listed, paraffingrade B will exhibit the most vigorous entrainment with a_(onset)=0.276.Lower melting point waxes n<31 will tend to entrain even morevigorously.

[0243] In summary, the present invention provides a high regression ratepropellant and a method for identifying such propellants that producehigh burning rates in hybrid rockets and other applications such assolid fuel ramjets. The propellant can be either a fuel or an oxidizer.The propellants are materials which form an unstable melt layer at theburning surface. Under the right conditions of port mass flux, liquidlayer surface tension, and viscosity, droplets may be entrained from theliquid layer into the high temperature gas flow in the port. The processis based on a criterion by which one can determine whether entrainmentwill occur for a given material.

[0244] The inventors have discovered that a class of non-cryogenic fuelswhich satisfies the required criterion is a certain range of n-alkanes.This range includes all paraffin waxes and polyethylene waxes. Morespecifically, we include alkanes having a carbon number of approximatelyn=15 to n=80. Other hydrocarbon compounds have also been identified thatsatisfy the required criterion. These include the alkhylnaphthalenes(including straight naphthalene), anthracene, and certain organic acids.These relatively dense materials can also be used as additives toparaffin based fuels. Mixtures of materials can also be used.

[0245] For example, paraffin wax can be easily mixed with polyethylene(PE) wax as well as carbon black and/or other common additives such asStearic acid.

[0246] The performance of a hybrid system can be optimized for a givenmission profile by mixing high and low molecular weight alkanes togetherto achieve the required regression rate.

[0247] The use of such a high burning rate fuel leads to a simplerhybrid rocket system wherein a single or double D port design can equalor exceed the performance of a conventional solid or liquid rocket.

[0248] While the present invention has been described primarily with usein hybrid rockets and ramjets, the present invention is suitable for usein many types of gas generation applications, such as auxiliary powerunits (APU), tank pressurization systems in liquid or hybrid rocketapplications, and turbine power generation systems.

[0249] As taught by the foregoing description, a greatly advanced hybridpropulsion system and a method has been provided by the presentinvention. The foregoing description of specific embodiments andexamples of the invention have been presented for the purpose ofillustration and description, and although the invention has beenillustrated by certain of the preceding examples, it is not to beconstrued as being limited thereby. Many modifications, embodiments andvariations are possible in light of the above teaching. It is intendedthat the scope of the invention encompass the generic area as hereindisclosed, and by the claims appended hereto and their equivalents.

1. A fuel composition suitable for use in hybrid rockets and solid fuelramjets or gas generation, comprising: a fuel disposed in a combustionchamber and means for causing the flow of an oxidizer past the fuel tocause combustion with a flame, characterized in that under the heattransfer from the flame, the fuel forms an unstable melt layer withviscosity and surface tension such that the melted fuel forms dropletsthat can be entrained in the oxidizer flow thereby increasing the rateof burning of the fuel.
 2. The fuel composition of claim 1 wherein thefuel is selected from the n-alkane class of hydrocarbons and mixturesthereof, having the general formula of C_(n)H_(2n+2), where n is a meancarbon number and is in the range of 15 to 80, and which are solid atroom temperature.
 3. The fuel composition of claim 1 wherein the fuel isselected from the n-alkane class of hydrocarbons and mixtures thereof,having the general formula of C_(n)H_(2n+2), where n is a mean carbonnumber and is in the range of 18 to
 40. 4. The fuel composition of claim1 wherein the fuel is comprised of a material where the viscosity of themelt layer is less than about 1 mPa-sec at an average temperaturebetween the melting and vaporization temperatures of the material, andthe surface tension of the melt layer is less than about 25 mN/m at theinterface temperature T_(interface).
 5. The fuel composition of claim 2wherein the fuel is selected from isomers of said alkane class ofhydrocarbons.
 6. The fuel composition of claim 1 wherein the fuel isselected from the group of alkhylnaphthalene compounds, anthracene andmixtures thereof.
 7. The fuel composition of claim 1 wherein the fuel isselected from the group of organic acids having the general formula ofCH₃(CH₂)_(n)COOH and mixtures thereof, where n is in the range of 8 to25.
 8. The fuel composition of claim 1 wherein the fuel is selected fromthe group of n-paraffin compounds and mixtures thereof.
 9. The fuelcomposition of claim 1 wherein said fuel component further includes oneor more additives selected from the group of alcohols, amines, organicacids, carbon black, and mixtures thereof.
 10. The fuel composition ofclaim 1 wherein said fuel component further includes carbon black at aconcentration in the range of about 0.2 to 2.0 weight percent.
 11. Thefuel composition of claim 1 wherein said fuel component is comprised ofa mixture of one or more paraffin waxes and carbon black in the range ofabout 0.2 to 2.0 weight percent.
 12. The fuel composition of claim 1wherein said fuel component is comprised of a mixture of one or moreparaffin waxes and one or more polyethylene waxes, or other highmolecular weight synthetic waxes.
 13. The fuel composition of claim 1wherein said fuel component further includes one or more additives toenhance the mechanical properties of said fuel.
 14. A method ofselecting a propellant that exhibits desirable regression rate duringcombustion within a port having a gas stream flowing through the port,comprising the steps of: determining for a given port mass flux,G=ρ_(g)U_(g), where ρ_(g) is the port average gas density and U_(g) isthe port average gas velocity; and determining for a thickness h of aliquid layer formed on the surface of said fuel; wherein said port massflux value and said thickness satisfy the relationship of: G ^(1.6) h^(0.6) ≧a _(onset), and where a_(onset) is the entrainment onsetparameter and is given by: a _(onset)=1.05×10⁻²[ρ_(g) ^(1.3)ρ_(l)^(0.3)][1/(Cf _(ref) C _(B1))^(0.8)](1/μ_(g))σμ₁ ^(0.6); and selectingsaid propellant such that a_(onset) has a value that promotesentrainment of droplets from said liquid layer into said gas streamflowing in said port, where the units of a_(onset) iskg^(1.65)/m^(2.3)−sec^(1.65).
 15. The method of claim 14 whereina_(onset) is equal to or less than approximately 0.9kg^(1.65)/m^(2.3)−sec^(1.65).
 16. The method of claim 14 wherein thepropellant is selected from the n-alkane class of hydrocarbons, havingthe general formula of C_(n)H_(2n+2) and mixtures thereof, where n is amean carbon number and is in the range of 15 to 80, and which are solidat room temperature.
 17. The method of claim 14 wherein the propellantis selected from the group of alkhylnaphthalene compounds, anthracene,and mixtures thereof.
 18. The method of claim 14 wherein the propellantis selected from the group of organic acids having the general formulaof CH₃(CH₂)_(n)COOH and mixtures thereof, where n is in the range of 8to
 25. 19. The method of claim 14 wherein the propellant is selectedfrom the group of n-paraffin compounds and mixtures thereof.
 20. Themethod of claim 14 wherein the propellant selected by said method is afuel or is an oxidant.
 21. The method of claim 14 wherein the propellantis selected from the group of isomers of the alkane class ofhydrocarbons.
 22. A propellant composition suitable for use in hybridrockets having a fuel component and an oxidizing component, where one ofsaid components flows past the other component, characterized in thatunder the heat of combustion the solid component forms an unstable meltlayer with viscosity and surface tension such that droplets melt layerare entrained in the gas stream thereby increasing the rate ofcombustion.
 23. The propellant of claim 22 wherein said propellant isused in solid fuel ramjets.
 24. The propellant of claim 22 wherein thefuel is selected from the n-alkane class of hydrocarbons, having thegeneral formula of C_(n)H_(2n+2) and mixtures thereof, where n is a meancarbon number and is in the range of 15 to 80, and which are solid atroom temperature.
 25. The propellant of claim 22 wherein the fuel isselected from the n-alkane class of hydrocarbons, having the generalformula of C_(n)H_(2n+2) and mixtures thereof, where n is a mean carbonnumber and is in the range of 18 to
 40. 26. The propellant of claim 22wherein the fuel is comprised of a material where the viscosity of themelt layer is less than about 1 mPa-sec at an average temperaturebetween the melting and vaporization temperatures of the material, andthe surface tension of the melt layer is less than about 25 mN/m at theinterface temperature T_(interface).
 27. The propellant of claim 22wherein the fuel is selected from the group of alkhylnaphthalenecompounds, anthracene and mixtures thereof.
 28. The fuel composition ofclaim 22 wherein the fuel is selected from the group of organic acidshaving the general formula of CH₃(CH₂)_(n)COOH and mixtures thereof,where n is in the range of 8 to
 25. 29. The propellant of claim 22wherein the fuel is selected from the group of n-paraffin compounds andmixtures thereof.
 30. The propellant of claim 22 wherein said fuelcomponent further includes one or more additives selected from the groupof alcohols, amines, organic acids, carbon black, and mixtures thereof.31. The propellant of claim 22 wherein said fuel component furtherincludes carbon black at a concentration in the range of about 0.2 to2.0 weight percent.
 32. The propellant of claim 22 wherein said fuelcomponent is comprised of a mixture of one or more paraffin waxes andcarbon black in the range of about 0.2 to 2.0 weight percent.
 33. Thepropellant of claim 22 wherein said fuel component is comprised of amixture of one or more paraffin waxes and one or more polyethylene waxesor other high molecular weight synthetic waxes.
 34. The propellant ofclaim 22 wherein said fuel component further includes one or morestiffening agents.
 35. A propulsion system including a structureterminating in a nozzle and having a fuel component within thestructure, one or more ports formed within, or containing, the fuelcomponent, and an oxidant vessel within the vehicle structure forflowing oxidant in contact with said one or more ports to combust saidfuel component, characterized in that the fuel is selected such thatunder the heat of combustion, the fuel forms an unstable melt layer withviscosity and surface tension such that droplets of the melted fuel areentrained in the flowing oxidant thereby enhancing the burning rate ofthe fuel.
 36. The propulsion system of claim 35 wherein the fuel isselected from the n-alkane class of hydrocarbons, having the generalformula of C_(n)H_(2n+2) and which are solid at room temperature. 37.The propulsion system of claim 35 wherein the fuel is selected from then-alkane class of hydrocarbons, having the general formula ofC_(n)H_(2n+2) and mixtures thereof.
 38. The propulsion system of claim35 wherein the fuel is comprised of a material where the viscosity ofthe melt layer is less than about 1 mPa-sec at an average temperaturebetween the melting and vaporization temperatures of the material, andthe surface tension of the melt layer is less than about 25 mN/m at theinterface temperature T_(interface).
 39. The propulsion system of claim35 wherein the fuel is selected from the group of alkhylnaphthalenecompounds, anthracene and mixtures thereof.
 40. The propulsion system ofclaim 35 wherein the fuel is selected from the group of organic acidshaving the general formula of CH₃(CH₂)_(n)COOH and mixtures thereof,where n is in the range of 8 to
 25. 41. The propulsion system of claim35 wherein the fuel is selected from the group of n-paraffin compoundsand mixtures thereof.
 42. The propulsion system of claim 35 wherein saidfuel component further includes one or more additives selected from thegroup of alcohols, amines, organic acids, carbon black, and mixturesthereof.
 43. The propulsion system of claim 35 wherein said fuelcomponent further includes carbon black at a concentration in the rangeof about 0.2 to 2.0 weight percent.
 44. The propulsion system of claim35 wherein said fuel component is comprised of a mixture of one or moreparaffin waxes and carbon black in the range of about 0.2 to 2.0 weightpercent.
 45. The propulsion system of claim 35 wherein said fuelcomponent is comprised of a mixture of one or more paraffin waxes andone or more polyethylene waxes or other high molecular weight syntheticwaxes.
 46. The propulsion system of claim 35 wherein said fuel componentfurther includes one or more stiffening agents.
 47. A combustible hybridfuel having a solid fuel component, and a flowing oxidizing componentflowing through a port in the solid fuel component, characterized inthat: said solid fuel component is comprised substantially of one ormore materials that form a liquid layer at the interface between theflowing oxidizing component and the solid fuel component duringcombustion by the oxidizing component, and wherein said liquid layerexhibits entrainment of liquid droplets in the flowing oxidizingcomponent during combustion at an entrainment rate expressed as:$\begin{matrix}{{\overset{.}{r}}_{e} \propto \frac{\left( {C_{f}P_{d}} \right)^{\alpha}h^{\beta}}{\sigma^{\gamma}\mu_{l}^{\delta}}} & (23)\end{matrix}$

where r_(e) is the empirical expression for the entrainment rate of theliquid droplets, P_(d) is a dynamic pressure of the oxidizing componentflow in the port, h is the thickness of the liquid layer, μ is theviscosity of the liquid layer, and σ is the surface tension of theliquid layer, and β is approximately 2, α is approximately 1.5, and γand δ are both approximately
 1. 48. The method of claim 14 used toselect a propellant that will exhibit a regression rate tailored to aparticular application or mission.